Let $f(x) = -5x^{2}+6x+2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Answer: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-5x^{2}+6x+2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -5, b = 6, c = 2$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot -5 \cdot 2}}{2 \cdot -5}$ $ x = \dfrac{-6 \pm \sqrt{76}}{-10}$ $ x = \dfrac{-6 \pm 2\sqrt{19}}{-10}$ $x =\dfrac{-3 \pm \sqrt{19}}{-5}$